Les math\'ematiques de la langue : l'approche formelle de Montague

TL;DR

This paper explores Montague's formal semantics, a mathematical approach to modeling natural language that employs formal languages, logic, type theory, and lambda calculus to understand linguistic meaning.

Contribution

It introduces Montague's formal semantics and the mathematical tools he used, providing insights into the mathematical foundation of natural language modeling.

Findings

Detailed explanation of Montague's formal semantics

Illustration of mathematical tools in language modeling

Educational overview of formal language and logic applications

Abstract

We present a natural language modelization method which is strongely relying on mathematics. This method, called "Formal Semantics," has been initiated by the American linguist Richard M. Montague in the 1970's. It uses mathematical tools such as formal languages and grammars, first-order logic, type theory and $\lambda$-calculus. Our goal is to have the reader discover both Montagovian formal semantics and the mathematical tools that he used in his method. ----- Nous pr\'esentons une m\'ethode de mod\'elisation de la langue naturelle qui est fortement bas\'ee sur les math\'ematiques. Cette m\'ethode, appel\'ee {\guillemotleft}s\'emantique formelle{\guillemotright}, a \'et\'e initi\'ee par le linguiste am\'ericain Richard M. Montague dans les ann\'ees 1970. Elle utilise des outils math\'ematiques tels que les langages et grammaires formels, la logique du 1er ordre, la th\'eorie de types et le $\lambda$-calcul. Nous nous proposons de faire d\'ecouvrir au lecteur tant la s\'emantique formelle de Montague que les outils math\'ematiques dont il s'est servi.